Find two numbers such that one number is 3 less than twice as big as the other number and the two numbers sum to 21.

Combining the like terms, the equivalent expression is given as follows:

-x + 25.

To add polynomials, we combine the like terms, that is, those with the same variable and exponent.

In this problem, the expression is:

(2x + 10) + (-3x + 15).

2x + 10 - 3x + 15

Combining the like terms:

2x - 3x + 10 + 15 = -x + 25.

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Answer:

I think the answer is B.36

Step-by-step explanation:

hope this helps if not let me know have a blessed day

The man paid $ 25.5 for the use of money.

The amount repaid to the bank on the due date is $3425.5

Calculating the amount of simple interest that will be charged on a loan can be done quickly and easily using the simple interest formula. To compute simple interest, multiply the principle, the number of days between payments, and the daily interest rate.

Principal(P)=$3400

Time(T)=3 months=1/4 yrs

Rate(R)=3%

The simple interest and final amount are calculated as follows:

Simple Interest(SI)=P*R*T/100

                               [tex]=\frac{3400*3*\frac{1}{4} }{100}[/tex]

                               =25.5

Net amount repaid=P+SI

                               =3400+25.5

                               =3425.5

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[tex]\angle BAD=100^{\circ}[/tex] (opposite angles in a parallelogram)

[tex]\angle EAD=80^{\circ}[/tex] (subtraction)

[tex]\angle ADE=65^{\circ}[/tex] (angles in a triangle add to 180 degrees)

[tex]\angle CDA=80^{\circ}[/tex] (adjacent angles in a parallelogram are supplementary)

[tex]\boxed{\angle CDE=15^{\circ}}[/tex] (subtraction)

[tex]\angle CED=65^{\circ}[/tex] (angles in a triangle add to 180 degrees)

[tex]\boxed{\angle AEB=80^{\circ}}[/tex] (angles on a straight line add to 180 degrees)

The graphs and their inequalities are

The inequalities are given as:

2x - 7y ≤ 14

7x + 2y ≥ 14

2x - 7y ≥ 14

3x + 4y < 6

4x - 3y > 6

3x + 4y > 6

To represent the inequalities on a graph, we use the following guides:

Using the above as a guide, we have:

Graph 1 ⇒ 3x + 4y > 6

Graph 2 ⇒ 2x - 7y ≥ 14

Graph 3 ⇒ 3x + 4y < 6

Graph 4 ⇒ 7x + 2y ≥ 14

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The domain of the function is (-∞, 1) U(1, ∞) while the domains are values greater than or equal to 1 that is y ≥1

The domain are independent variable for which the equation exist while the range are dependent variable for which the equation exist

Given the following functions

f(x) =2/x-1

g(x) = x+1

Determine  (g ○ f)(x)

(g ○ f)(x) = g(f(x))

(g ○ f)(x) = g(2/x-1)

(g ○ f)(x) = (2/x-1) + 1

(g ○ f)(x) = 2+(x-1)/x-1

(g ○ f)(x) = x+1/x-1

Hence the domain of the function is (-∞, 1) U(1, ∞) while the domains are values greater than or equal to 1 that is y ≥1

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The height and the radius that minimize the material needed to manufacture the can is 4.18336 cm and 4.18337 cm respectively.

Computed using differentiation.

We assume the radius of the can be r cm, and its height to be h cm.

We are given that the can is to hold 230 cm³ of liquid, thus the volume of the can is:

V = 230,

or, πr²h = 230 {Since, the volume of a cylinder is πr²h, where r is the radius, and h is the height},

or, h = 230/(πr²) ... (i) .

We are asked to find the height and radius that minimize the amount of the material.

To calculate the amount of the material, we calculate the surface area of the can (A).

The surface area of the can = area of the base + area of the side,

or, A = πr² + 2πrh = πr(r + 2h).

Substituting h = 230/(πr²), we get:

A = πr(r + 2{230/(πr²)}),

or, A = {πr(πr³ + 460)}/πr² = πr² + 460/r.

Differentiating both sides with respect to the radius r, we get:

dA/dr = 2πr - 460/r² ...(ii)

To find the point of inflection, we equate this to zero, to get:

2πr - 460/r² = 0,

or, 2πr = 460/r²,

or, r³ = 460/2π = 73.2113,

or, r = 4.18337 cm.

To check whether the point of inflection shows the point of maximum or minimum, we differentiate (ii) with respect to the radius r, to get:

d²A/dr² = 2π + 920/r³, which is always positive when the radius r is positive.

Thus, the area is minimum when the radius r = 4.18337 cm.

Height, h = 230/(πr²) = 4.18336 cm.

Thus, the height and the radius that minimize the material needed to manufacture the can is 4.18336 cm and 4.18337 cm respectively.

Computed using differentiation.

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[tex]\Large\maltese\underline{\textsf{A. \space What is Asked}}[/tex]

Find the gradient of the line segment between the points [tex]\bf{(4,3)\:and\:(5,6)}[/tex]

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

The formula used, here is

[tex]\bf{m=\dfrac{y2-y1}{x2-x1}[/tex]

[tex]\cline{1-2}[/tex]

Now let's put in the co-ordinates from these two points.

[tex]\bf{m=\dfrac{6-3}{5-4}}[/tex] | subtract on top & bottom

[tex]\bf{m=\dfrac{3}{1}}[/tex] | divide

[tex]\bf{m=3}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

                      [tex]\bf{=m=3}[/tex]

[tex]\boxed{\bf{ aesthetic\not101}}[/tex]

Answer:

g=3

Step-by-step explanation:

gradient=change ofY/change of X

3-6/4-5

-3/-1 simply

gradient =3

Kenyan formula easy

The result of the mathematical expression given as follows: (1/2 + 3/2)² + (2/3 x 1/2)³ is 5.59 or 5⅔.

According to this question, the following expression is given to solve: (1/2 + 3/2)² + (2/3 x 1/2)³

First, we solve the both parts as follows:

Next, we solve the exponential function as follows:

= (2)² + (1.16)³

= 4 + 1.59

= 5.59 or 5⅔

Therefore, the result of the mathematical expression given as follows: (1/2 + 3/2)² + (2/3 x 1/2)³ is 5.59 or 5⅔.

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Answer: Quadratic

Step-by-step explanation:

I'm too lazy to explain. Trust me

The wrestler's weight before he went on his diet is 78 kg

The formula for slope is;

m = (y2 - y1)/(x2 - x1)

Thus, using two points we have;

m = (93.6 - 85.8)/(3 - 1.5)

m = 5.2

At the start of his diet, time in months = 0 months and so x = 0. Thus;

5.2 = (85.8 - y0)/(1.5 - 0)

5.2 * 1.5 = 85.8 - y0

y0 = 85.8 - (5.2 * 1.5)

y0 = 85.8 - 7.8

y0 = 78 kg

Thus, the wrestler's weight before he went on his diet is 78 kg

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The range of a function is all possible y values that a function can take on.

In the case of the given function, the y values fluctuate between -1 and 1. Therefore, the range of the function is -1 <= y <= 1 (Option A).

Hope this helps!

The correct option is:

As the x-values go to positive infinity, the function's values go to positive infinity.

By the description, We know that the function has the points:

(-1.25, -3.25), (0.25, -1.75) (-2.25, 0), (0, -2), (-2.75, 6), (1.5, 6)

Notice that from x = 0.25 to x = 1.5 the function goes upwards, then in the right side, the function goes up, so as x goes to positive infinity, also does f(x).

On the left side, we can see  that from x = -2.75 to x = -2.25 the function goes downwards.

So, as x goes to the left (negative infinity) f(x) goes upwards.

Then as x tends to negative infinity, f(x) tends to infinity.

The correct option is:

As the x-values go to positive infinity, the function's values go to positive infinity.

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Answer:

D

Step-by-step explanation:

edge 23

Answer:

B

Step-by-step explanation:

Michelangelo went 30 feet for a pizza to a pizza restaurant.

It is given that,

Michelangelo was starving for a slice of pizza. He started -50 feet in the sewer, climbed the ladder to the street, and ran 20 feet to the pizza restaurant.

So, the total feet he traveled is,

= -50 feet + 20 feet = 30 feet.

Therefore, Michelangelo went 30 feet for pizza.

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Answer:

(0,-0)

Step-by-step explanation:

P(0,0)=P(0,-0)

Answer: D: SSS Congruency

Step-by-step explanation:

- SSS congruency stands for side-side-side congruency

- if the 3 side lengths are equal for both triangles they are equivalent

- the reflexive property states that an angle, line segment, or shape is always congruent to itself

- so the reflexive property is just saying that WY = YW, therefore creating 3 equal sides for both triangles

- so the triangles are congruent by SSS

hope this helps :)

For Ms. Cho's class, the formula is =randBetween(1,21). The result of interest is 14 or less.

12/20 reduces to 4/5 --> 4/5 of 15 is 12.

So using the spinner to model Mr. Skinner's class, an outcome of the select 12 sections of interest represent, symbolize, and model a student bringing lunch from home.

LIkewise, 14/21 reduces to 2/3 --> 2/3 of 15 is 10.

So using the spinner to model Ms. CHo's class, an outcome of only 10 of the 15 sections of interest represent, model, and symbolize a student who brings lunch from home.

The same can be done in Excel: The function is =randBEtween( minVal, maxVal)

For example =randBetween(1,20) will model Mr. Skinner's class. A result of 12 or less represents, model, simulates, and symbolizes a student who packed their lunch.

For Ms. Cho's class, the formula is =randBetween(1,21). The result of interest is 14 or less.

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Answer:

f(g(-2)) = -3

Step-by-step explanation:

g(-2) = -2 - 3 = -5

f(-5) = 2(-5) + 7 = -10 + 7 = -3

Answer:

17.2°

Explanations

To find angle A, use the cosine rule.

a^2 = b^2 + c^2 - 2 × a × c cos A

4^2 = 7^2 + 10^2 - 2 × 7 × 10 cos A

16 = 49+ 100 - 140 × cosA

16 = 149 - 140cosA

16- 149 = - 140cosA

-133 = - 140cosA

cosA = 133/140

cosA = 0.95

A = 17.2°

Answer:

obtuse because 62 + 102 < 122

S

its c, obtuse, becuase 6^2+10^2<12^2

Answer:

Step-by-step explanation:

Using the binomial distribution, the probabilities are given as follows:

a. 0.2637 = 26.37%.

b. 0.8965 = 89.65%.

c. 0.0148 = 1.48%.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of the parameters for this problem are:

n = 5, p = 0.25.

Item a:

The probability is P(X = 2), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{5,2}.(0.25)^{2}.(0.75)^{3} = 0.2637[/tex]

Item b:

The probability is:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{5,0}.(0.25)^{0}.(0.75)^{5} = 0.2373[/tex]

[tex]P(X = 1) = C_{5,1}.(0.25)^{1}.(0.75)^{4} = 0.3955[/tex]

[tex]P(X = 2) = C_{5,2}.(0.25)^{2}.(0.75)^{3} = 0.2637[/tex]

Then:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2373 + 0.3955 + 0.2637 = 0.8965[/tex]

Item c:

The probability is:

[tex]P(X \geq 4) = P(X = 4) + P(X = 5)[/tex]

In which:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 4) = C_{5,4}.(0.25)^{4}.(0.75)^{1} = 0.0147[/tex]

[tex]P(X = 5) = C_{5,1}.(0.25)^{5}.(0.75)^{0} = 0.0001[/tex]

Then:

[tex]P(X \geq 4) = P(X = 4) + P(X = 5) = 0.0147 + 0.0001 = 0.0148[/tex]

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Answer:

24.8°

Step-by-step explanation:

Complementary angles sum 90°

65.2° + B° = 90°

B° = 90° - 65.2°

B° = 24.8

Angle B from the information given is 24. 8°

Note that complementary angles sum up to 90°

From the information given, we have that

Angle A + Angle B = 90°

If angle A = 65. 2°

Angle B = 90 - 65. 2

Angle B = 24.8°

Thus, angle B from the information given is 24. 8°

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Answer:

Drag and drop 6(2x-1) to 12x-6.

Drag and drop 6(4x-2) to Neither.

Drag and drop 3(8x+4) to 24x+12.

Drag and drop 6(4x+2) to 24x+12.

Drag and drop 2(6x-3) to 12x-6.

Step-by-step explanation:

To check these, use distributive property to solve each one.

6(2x-1) = 12x-6

6(4x-2) = 24x-12

3(8x+4) = 24x+12

6(4x+2) = 24x+12

2(6x-3) = 12x-6

Hope this helps!

Please mark brainliest! Thanks!

Answer:

a

Step-by-step explanation:

Based on the two-tangent theorem, the measure of TH is also: 4.2 cm.

According to the two-tangent theorem, the length of two tangents (TG and TH) that are drawn from a circle to intersect at an external point are equal. That is, they are congruent to each other.

Thus, we are given that, TG = 4.2 cm. Therefore, based on the two-tangent theorem, the measure of TH is also: 4.2 cm.

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Answer:

A brush: $4.50

A tube of paint: $2

Step-by-step explanation:

Let b = brushes

Let p = paint

1) Set up equations.

4b + 7p = 32

6b + 8p = 43

2) Solve the system of equations using elimination.

(4b + 7p = 32)3

(6b + 8p = 43)2

-----------------------

12b + 21p = 96

12b + 16p = 86

----------------------

5p = 10

p = 10/5

p = 2

Substitute 2 into p of any of the two equations.

4b + 7(2) = 32

4b + 14 = 32

4b = 32 - 14

4b = 18

b = 18/4

b = 4.50

Therefore, a brush costs $4.50, while a tube of paint costs $2.

The congruency statement that describes the figure is: D. ΔRST ≅ ΔBAC.

A congruency statement is a statement that states that two triangles are congruent to each other.

180 degrees rotation around the origin will give us the rule: (x, y) → (-x, -y)

Therefore, applying this rule to triangle RST that was rotated, we would have:

R'(-1, -1)

S'(-3, -4)

T'(-5, 0)

Translating R'S'T' 3 units up, using the rule, (x, y + 3) will give us:

B(-1, 2)

A(-3, -1)

C(-5, 3)

Therefore, we can conclude that, D. ΔRST ≅ ΔBAC.

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Answer:its D just took test:)

Step-by-step explanation: